Michael has substantial student debt, but he recently got a new job, which came with a signing bonus. He calculates that with his new job, he can put aside a fixed amount of money every month to pay off his debt. He also puts the entirety of his bonus towards paying off his debt. He constructs the expression 36,700 - (5,000 + 500m) to represent the size of his debt after m months. Which number describes the value of his signing bonus?
(1 point)
Responses
36,000
36,000
5,000
5,000
500
500
Which statement about the product is true?
6.57 x 2.67534
(1 point)
Responses
The product is irrational.
The product is irrational.
The product is rational.
The product is rational.
The product is neither rational nor irrational.
The product is neither rational nor irrational.
The nature of the product cannot be determined.
The product is rational.
In which of these situations, do the two quantities combine to make 0? Select all that apply.
(1 point)
Responses
An airplane at 3,000 feet gains 3,000 feet.
An airplane at 3,000 feet gains 3,000 feet.
A submarine at –340 feet under dives 340 feet.
A submarine at –340 feet under dives 340 feet.
A hawk at 120 feet above the ground dives 120 feet.
A hawk at 120 feet above the ground dives 120 feet.
A diver at –40 feet under the sea rises 40 feet.
A diver at –40 feet under the sea rises 40 feet.
An octopus at –38 feet underwater rises 38 feet.
An octopus at –38 feet underwater rises 38 feet.
A submarine at –340 feet under dives 340 feet.
A diver at –40 feet under the sea rises 40 feet.
An octopus at –38 feet underwater rises 38 feet.
To determine the value of Michael's signing bonus, we need to solve the expression 36,700 - (5,000 + 500m) where m represents the number of months.
Since Michael puts the entirety of his bonus towards paying off his debt, we can compare the expression with the given information. Michael has a new job with a signing bonus, meaning the expression should equal zero after substituting the appropriate values.
Therefore, we can set up the equation:
36,700 - (5,000 + 500m) = 0
To solve for m, we first simplify the equation:
36,700 - 5,000 - 500m = 0
31,700 - 500m = 0
Next, we isolate the variable:
-500m = -31,700
m = (-31,700) / (-500)
m = 63.4
Since m represents the number of months, we cannot have a fraction of a month. Therefore, we can conclude that the value of his signing bonus is 36,700 - (5,000 + 500 * 63) = 36,700 - (5,000 + 31,500) = 36,700 - 36,500 = 200.
Thus, the number that describes the value of his signing bonus is 200.
To find out the value of Michael's signing bonus, we need to understand the expression that represents the size of his debt after m months. In the expression "36,700 - (5,000 + 500m)", the term "(5,000 + 500m)" represents the amount of money Michael has put aside from his monthly savings after m months. This means that the remaining amount, "36,700 - (5,000 + 500m)", represents his debt.
Since the signing bonus is the amount Michael is putting entirely towards paying off his debt, it is the initial amount that he owes, which is the total debt before he starts making monthly payments. To find it, we can simplify the expression by removing the terms related to his monthly savings:
36,700 - (5,000 + 500m)
= 36,700 - 5,000 - 500m
= 31,700 - 500m
So, the initial debt before he starts making monthly payments is 31,700. Therefore, the number that describes the value of his signing bonus is 31,700.